Time lags and emergent stability in morphogenic/pedogenic system models

The balance between pedogenic forces operating normal to and morphogenic forces operating tangent to the land surface is critical to landscape stability and evolution. A simple nonlinear first-order difference model of the slope mass balance for a unit area along a hillslope shows chaotic behavior when morphogenesis and pedogenesis are in phase, such that there is no lag between debris production and its availability for removal. However, when morphogenesis and pedogenesis are out of phase, the model is stable and nonchaotic. The lagged, out-of-phase version of the model produces a stable equilibrium thickness of soil/regolith cover, no matter what parameter values are used to describe rates of morphogenic and pedogenic processes or the feedbacks between pedogenic processes and regolith thickness. This model shows that inclusion of a simple one-increment lag with no other changes in model structure can produce qualitatively different results, which are especially striking in the spatial domain. Whereas lags in geomorphic and pedologic systems (and in nonlinear dynamical systems in general) have generally been viewed as sources of instability and chaos, in this case the inclusion of a lag leads to stability. The emergence of stability at broader spatial scales may thus be linked to lag effects, rather than to spatial averaging.